Gen Tatara, Hiroshi Kohno, Junya Shibata
Microscopic theory of domain wall dynamics under electric current is reviewed. Domain wall is treated as rigid and planar. The spin-transfer torque and forces on the wall are derived based on the $s$-$d$ exchange interaction between localized spins and conduction electrons, treating non-adiabaticity expressed by the gauge field perturbatively. Effect of spin relaxation is also studied.
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The spin transfer torque generated by a spin-polarized current can induce the shift of the magnetic domain-wall position. In this work, we study theoretically the current-induced domain-wall motion by using the collective coordinate approach [Gen Tatara and Hiroshi Kohno, Phys. Rev. Lett. 92, 86601 (2004)]. The approach is extended to include not only the domain-wall position and the polarization angle changes but also the domain-wall width variation. It is demonstrated that the width variation affects the critical current.
We numerically demonstrate that domain walls can be used as spin wave waveguides. We show that gapless spin waves bounded inside a domain wall can be guided by the domain wall. For Bloch walls, we further show that the bound spin waves can pass through Bloch lines and corners without reflection. This finding makes domain-wall-based spin wave devices possible.
We study transport through ballistic and diffuse ferromagnetic domain walls in a two-band Stoner model with a rotating magnetization direction. For a ballistic domain wall, the change in the conductance due to the domain wall scattering is obtained from an adiabatic approximation valid when the length of the domain wall is much longer than the Fermi wavelength. In diffuse systems, the change in the resistivity is calculated using a diagrammatic technique to the lowest order in the domain wall scattering and taking into account spin-dependent scattering lifetimes and screening of the domain wal…
The mechanism of the parametrical stimulated tunneling in the spectrum of the moving domain wall considered. It is shown that such a mechanism can to cause the initial phase of the parametrical evolution of domain wall's surface waves. In turn, this evolution leads to an appearance of essential features in domain walls dynamics.
Manipulation of magnetic domain walls via a helicity-independent laser pulse has recently been experimentally demonstrated and various physical mechanisms leading to domain wall dynamics have been discussed. Spin-dependent superdiffusive transport of hot electrons has been identified as one of the possible ways how to affect a magnetic domain wall. Here, we develop a model based on superdiffusive spin-dependent transport to study the laser-induced transport of hot electrons through a smooth magnetic domain wall. We show that the spin transfer between neighboring domains can enhance ultrafast d…
We study the domain wall motion in a disordered weak ferromagnet, induced by injecting a spin current from a strong ferromagnet. Starting from the spin diffusion equation describing the spin accumulation in the weak ferromagnet, we calculate the force and torque acting on the domain wall. We also study the ensuing domain wall dynamics, and suggest a possible measurement method for detecting the domain wall motion via measuring the additional resistance.
We investigated how the dynamics of a domain wall are affected by the presence of spin density waves in a ferromagnetic wire. Domain walls and other scattering centres can cause coherent spin density waves to propagate through a wire when a current is applied. In some cases the spin torque due to these scattered electrons can be enhanced such that it is on a par with the exchange and anisotropy energies controlling the shape and dynamics of the domain wall. In such a case we find that the spin density waves enhance the current induced domain wall motion, allowing for domain wall motion with sm…
We report a study on the field-driven propagation of vortex-like domain walls in ferromagnetic nanotubes. This particular geometry gives rise to a special feature of the static wall configuration, which significantly influences its dynamics. Unlike domain walls in flat strips, the left-right symmetry of domain wall propagation is broken. Furthermore, the domain wall velocity is not limited by the Walker breakdown. Under sufficiently large magnetic fields, the domain wall velocity reaches the velocity of spin waves (about 1000 m/s) and is thereafter connected with a direct emission of spin wave…
The pinning phenomena of the domain wall in the presence of exchange bias is studied analytically. The analytic solution of the domain wall spin configuration is presented. Unlike the traditional solution which is symmetric, our new solution could exhibit the asymmetry of the domain wall spin profile. Using the solution, the domain wall position, its width, its stability, and the depinning field are discussed analytically.
We theoretically study a ferrimagnetic domain-wall motion driven by a rotating magnetic field. We find that, depending on the magnitude and the frequency of the rotating field, the dynamics of a ferrimagnetic domain wall can be classified into two regimes. First, when the frequency is lower than a certain critical frequency set by the field magnitude, there is a stationary solution for the domain-wall dynamics, where a domain-wall in-plane magnetization rotates in-phase with the external field. The field-induced precession of the domain wall gives rise to the translational motion of the domain…
In conventional domain wall systems the aim of a high domain wall velocity may be hindered by the occurrence of a Walker breakdown at comparably low current density. We show how a Rashba interaction can stabilize the domain wall dynamics and thereby shift the Walker breakdown to higher current densities. The Rashba interaction creates a field like spin torque, which breaks the symmetry of the system and modifies the internal structure of the domain wall. Besides a shift of the Walker breakdown it can additionally induce a chirality switch of the domain wall at sufficient Rashba fields. The pre…
We study shot noise of the spin-polarized current in a diffusive ferromagnetic nanowire which contains a ballistic domain wall. We find that the existence of a short domain wall influences strongly the shot noise for sufficiently high spin-polarization of the wire. Compared to the situation of the absence of the domain wall, the shot noise can be reduced or enhanced depending on the length of the domain wall and its relative conductance.
Momentum transfer from incoming magnons to a Bloch domain wall is calculated using one dimensional continuum micromagnetic analysis. Due to the confinement of the wall in space, the dispersion relation of magnons is different from that of a single domain. This mismatch of dispersion relations can result in reflection of magnons upon incidence on the domain wall, whose direct consequence is a transfer of momentum between magnons and the domain wall. The corresponding counteraction force exerted on the wall can be used for the control of domain wall motion through magnonic linear momentum transf…
Fast domain wall motion in systems with perpendicular magnetization is necessary for many novel applications such as the racetrack memory, domain wall logic devices and artificial synapses. The domain wall speed has been greatly improved after the demonstration of current driven domain wall motion using the spin transfer torque, and later achieved another leap due to the combined effect of spin-Hall effect and Dzyaloshinskii-Moriya interaction (DMI). However, only Neel wall can be effectively driven in the latter system. In this paper, we show that both Bloch and Neel domain walls can be effec…
We investigate how to facilitate the injection of domain walls in chiral ferromagnetic nanowires by electrical means. We calculate the critical current density above which domain walls are injected into the nanowire depending on the material parameters and the source of interaction including spin-transfer torques as well as spin-orbit torques. We demonstrate that the Dzyaloshinskii-Moriya interaction can significantly reduce the required critical current to inject the types of domain walls favored by the Dzyaloshinskii-Moriya interaction. We find that in chiral magnets it is only possible to s…
This is an intoduction to the theory of the essentially mesoscopic phenomena for the magnetic domain walls.
We report on the controllable pinning of domain walls in stripes with perpendicular magnetic anisotropy by magnetostatic coupling to magnetic vortices in disks located above the stripe. Pinning mechanisms and depinning fields are reported. This novel pinning strategy, which can be realized by current nanofabrication techniques, opens up new possibilities for the non-destructive control of domain wall mobility in domain wall based spintronic devices.
Magnetic domain walls can be moved by spin-polarized currents due to spin-transfer torques. This opens the possibility to use them in spintronic memory devices as, e.g., in racetrack storage. Naturally, in miniaturized devices domain walls can get very close to each other and affect each others dynamics. In this work we consider two separated domain walls in different layers which interact via an interlayer exchange coupling. One of these walls is moved by a spin-polarized current. Depending on several parameters as the current density, the interlayer coupling or the pinning potential, the com…
Domain walls in ferroelectrics exhibit a plethora of phases and functionalities not found in the bulk. The interplay of electrostatic, chemical, topological, and distortive inhomogeneities at the walls can be so complex, however, that this obstructs their technological performance. In tetragonal ferroelectrics like PbZrxTi1-xO3, for example, the desired functional 180° domain walls within out-of-plane-polarized c-domains are interspersed by in-plane-polarized a-domains and the associated network of domain walls remains challenging to analyze. Here we use a combination of STEM and optical secon…
We present a circuit model to describe the electron transport through a domain wall in a ferromagnetic nanowire. The domain wall is treated as a coherent 4-terminal device with incoming and outgoing channels of spin up and down and the spin-dependent scattering in the vicinity of the wall is modelled using classical resistances. We derive the conductance of the circuit in terms of general conductance parameters for a domain wall. We then calculate these conductance parameters for the case of ballistic transport through the domain wall, and obtain a simple formula for the domain wall magnetores…
Understanding the domain wall dynamics is an important issue in modern magnetism. Here we present results of domain wall displacement in curved cylindrical nanowires at a constant magnetic field. We show that the average velocity of a transverse domain wall increases with curvature. Contrary to what it is observed in stripes, in a curved wire the transverse domain wall oscillates along and rotates around the nanowire with the same frequency. These results open the possibility of new oscillation-based applications.
We investigate magnetic domain walls in a single fcc Mn layer on Re(0001) employing spin-polarized STM, atom manipulation, and spin dynamics simulations. The low symmetry of the row-wise antiferromagnetic (1Q) state leads to a new type of domain wall which connects rotational 1Q domains by a transient 2Q state with characteristic 90$^\circ$ angles between neighboring magnetic moments. The domain wall properties depend on their orientation and their width of about 2 nm essentially results from a balance of Heisenberg and higher-order exchange interactions. Atom manipulation allows domain wall i…
Scaling of Magnetic Domain Walls in Perpendicular Magnetic Anisotropy Systems
本研究通过分析和微磁模拟揭示了垂直磁各向异性系统中磁域壁宽度与DMI、交换刚度等参数的标度关系，明确了磁域壁类型随DMI变化的转变机制。
We analyze the equilibrium micromagnetic domain wall structures encountered in Permalloy strips of a wide range of thicknesses and widths, with strip widths up to several micrometers. By performing an extensive set of micromagnetic simulations, we show that the equilibrium phase diagram of the domain wall structures exhibits in addition to the previously found structures (symmetric and asymmetric transverse walls, vortex wall) also double vortex and triple vortex domain walls for large enough strip widths and thicknesses. Also several metastable domain wall structures are found for wide and/or…
Magnetic domain walls are objects whose dynamics is inseparably connected to their structure. In this work we investigate magnetic bilayers, which are engineered such that a coupled pair of domain walls, one in each layer, is stabilized by a cooperation of Dzyaloshinskii-Moriya interaction and flux-closing mechanism. The dipolar field mediating the interaction between the two domain walls, links not only their position but also their structure. We show that this link has a direct impact on their magnetic field induced dynamics. We demonstrate that in such a system the coupling leads to an incr…
The theory of elasticity and pinning of domain walls in helical magnets is presented. Domain walls perpendicular to the helical axis show non-local elasticity and are marginally pinned by local disorder. Weak anisotropy combined with magnetic dilution leads however to a non-local bulk pinning effect. Domain walls with other orientations include generically vortex arrays, similar to type-II superconductors. Their pinning force is calculated as a function of wall orientation, pitch angle and impurity concentration. It is shown that metastable domains can vary between needle and pancake like shap…
Simultaneous imaging of the piezoresponse phase, amplitude and bare surface topography of displacive ferroelectric thin films by scanning probe microscopy directly shows the nature of domain wall pinning and its relation to morphological disorder. Strong and stable pinning of walls occurs at grain boundaries while weak and unstable pinning occurs within the grains. The results show that polarization reversal consists of both nucleation of domains and spreading of domain walls, the latter being the dominant process in multi-grain regions. A characteristic single-grain switching in faceted grain…
We carry out large-scale micromagnetic simulations which demonstrate that due to topological constraints, internal domain walls (Bloch lines) within extended domain walls are more robust than domain walls in nanowires. Thus, the possibility of spintronics applications based on their motion channeled along domain walls emerges. Internal domain walls are nucleated within domain walls in perpendicularly magnetized media concurrent with a Walker breakdown-like abrupt reduction of the domain wall velocity above a threshold driving force, and may also be generated within pinned, localized domain wal…
Domain wall skyrmions are skyrmions trapped inside a domain wall. We investigate domain wall skyrmions in chiral magnets using a fully analytic approach. Treating the Dzyaloshinskii-Moriya (DM) interaction perturbatively, we construct the low-energy effective theory of a magnetic domain wall in an $O(3)$ sigma model with the DM interaction and an easy-axis potential term, yielding a sine-Gordon model. We then construct domain wall skyrmions as sine-Gordon solitons along the domain wall. We also construct domain wall skyrmions on top of a pair of a domain wall and an anti-domain wall. One of ch…
Charge resistance and spin torque are generated by coherent carrier transport through ferromagnetic 360 degree domain walls, although they follow qualitatively different trends than for 180 degree domain walls. The charge resistance of 360 degree domain walls reaches a maximum at an intermediate wall thickness, unlike 180 degree domain walls, whose resistance decreases monotonically with wall thickness. The peak amplitude of the spin torque and the optimal thickness of the domain wall to maximize torque for a 360 degree wall are more than twice as large as found for a 180 degree domain wall in…
Domain-wall skyrmion chain and domain-wall bimerons in chiral magnets
该研究在手性磁体中构建畴壁斯格明子链与畴壁双半子，解析结合数值分析其在铁磁相和手性孤子晶格中的稳定性，揭示尖点演化、衰变及稳定链形成规律。
We study the influence of oxygen vacancies on the formation of charged 180$^\circ$ domain walls in ferroelectric BaTiO$_3$ using first principles calculations. We show that it is favorable for vacancies to assemble in crystallographic planes, and that such clustering is accompanied by the formation of a charged domain wall. The domain wall has negative bound charge, which compensates the nominal positive charge of the vacancies and leads to a vanishing density of free charge at the wall. This is in contrast to the positively charged domain walls, which are nearly completely compensated by free…
We numerically compute current-induced spin-transfer torques for antiferromagnetic domain walls, based on a linear response theory in a tight-binding model. We find that, unlike for ferromagnetic domain wall motion, the contribution of adiabatic spin torque to antiferromagnetic domain wall motion is negligible, consistent with previous theories. As a result, the non-adiabatic spin-transfer torque is a main driving torque for antiferromagnetic domain wall motion. Moreover, the non-adiabatic spin-transfer torque for narrower antiferromagnetic domain walls increases more rapidly than that for fer…
Chiral domain walls of Neel type emerge in heterostructures that include heavy metal (HM) and ferromagnetic metal (FM) layers owing to the Dzyaloshinskii-Moriya (DM) interaction at the HM/FM interface. In developing storage class memories based on the current induced motion of chiral domain walls, it remains to be seen how dense such domain walls can be packed together. Here we show that a universal short range repulsion that scales with the strength of the DM interaction exists among chiral domain walls. The distance between the two walls can be reduced with application of out of plane field,…
The orientation of a chiral magnetic domain wall in a racetrack determines its dynamical properties. In equilibrium, magnetic domain walls are expected to be oriented perpendicular to the stripe axis. We demonstrate the appearance of a unidirectional domain wall tilt in out-of-plane magnetized stripes with biaxial anisotropy and Dzyaloshinskii--Moriya interaction (DMI). The tilt is a result of the interplay between the in-plane easy-axis anisotropy and DMI. We show that the additional anisotropy and DMI prefer different domain wall structure: anisotropy links the magnetization azimuthal angle …
Transport through zincblende magnetic semiconductors with magnetic domain walls is studied theoretically. We show that these magnetic domain walls have an intrinsic resistance due to the spin-orbit interaction. The intrinsic resistance is independent of the domain wall shape and width when the latter is larger than the Fermi wavelength. For typical parameters, the intrinsic domain wall resistance is comparable to the Sharvin resistance and should be experimentally measurable.
We have studied the domain wall resistance in W/Ta/CoFeB/MgO heterostructures. The Ta layer thickness is varied to control the type of domain walls via changes in the interfacial Dzyaloshinskii Moriya interaction. We find a nearly constant domain wall resistance against the Ta layer thickness. Adding contributions from the anisotropic magnetoresistance, spin Hall magnetoresistance and anomalous Hall effect describe well the domain wall resistance of the thick Ta layer films. However, a discrepancy remains for the thin Ta layer films wherein chiral Néel-like domain walls are found. These result…
We have investigated the domain wall resistance for two types of domain walls in a (Ga,Mn)As Hall bar with perpendicular magnetization. A sizeable positive intrinsic DWR is inferred for domain walls that are pinned at an etching step, which is quite consistent with earlier observations. However, much lower intrinsic domain wall resistance is obtained when domain walls are formed by pinning lines in unetched material. This indicates that the spin transport across a domain wall is strongly influenced by the nature of the pinning.
We study theoretically hole current-driven domain wall dynamics in (Ga,Mn)As. We show that the spin-orbit coupling causes significant hole reflection at the domain wall, even in the adiabatic limit when the wall is much thicker than the Fermi wavelength, resulting in spin accumulation and mistracking between current-carrying spins and the domain wall magnetization. This increases the out-of-plane non-adiabatic spin transfer torque and consequently the current-driven domain wall mobility by three to four orders of magnitude. Trends and magnitude of the calculated domain wall current mobilities …
Magnetic moments in atomic scale domain walls formed in nanoconstrictions and nanowires are softened which affects dramatically the domain wall resistance. We perform ab initio calculations of the electronic structure and conductance of atomic-size Ni nanowires with domain walls only a few atomic lattice constants wide. We show that the hybridization between noncollinear spin states leads to a reduction of the magnetic moments in the domain wall. This magnetic moment softening strongly enhances the domain wall resistance due to scattering produced by the local perturbation of the electronic po…
Searching for new methods controlling antiferromagnetic (AFM) domain wall is one of the most important issues for AFM spintronic device operation. In this work, we study theoretically the domain wall motion of an AFM nanowire, driven by the axial anisotropy gradient generated by external electric field, allowing the electro control of AFM domain wall motion in the merit of ultra-low energy loss. The domain wall velocity depending on the anisotropy gradient magnitude and intrinsic material properties is simulated based on the Landau-Lifshitz-Gilbert equation and also deduced using the energy di…
We explore a new type of domain wall structure in ultrathin films with perpendicular anisotropy, that is influenced by the Dzyaloshinskii-Moriya interaction due to the adjacent layers. This study is performed by numerical and analytical micromagnetics. We show that these walls can behave like Neel walls with very high stability, moving in stationary conditions at large velocities under large fields. We discuss the relevance of such walls, that we propose to call Dzyaloshinskii domain walls, for current-driven domain wall motion under the spin Hall effect.
A special cross-tie (SCT) domain wall was discovered in the helimagnet MnCoSi alloy via the magnetic vector field tomography in Lorentz transmission electron microscopy (LTEM). Different to the traditional cross-tie (TCT) domain wall where the convergent/divergent magnetic moment configuration line up one by one, the relative large Bloch type sub-walls emerge in this brand-new SCT domain wall and two mutually perpendicular rotation axes coexist in this special feature. The straight magnetic stripes accompanied with the unraveled domain walls hint the complex mechanism to form this SCT structur…
We demonstrate optical manipulation of the position of a domain wall in a dilute magnetic semiconductor, GaMnAsP. Two main contributions are identified. Firstly, photocarrier spin exerts a spin transfer torque on the magnetization via the exchange interaction. The direction of the domain wall motion can be controlled using the helicity of the laser. Secondly, the domain wall is attracted to the hot-spot generated by the focused laser. Unlike magnetic field driven domain wall depinning, these mechanisms directly drive domain wall motion, providing an optical tweezer like ability to position and…
Current-driven vortex wall dynamics is studied by means of a two-dimensional analytical model and micromagnetic simulation. By constructing a trial function for the vortex wall in the magnetic wire, we analytically solve for domain wall velocity and deformation in the presence of the current-induced spin torque. A critical current for the domain wall transformation from the vortex wall to the transverse wall is calculated. A comparison between the field- and current-driven wall dynamics is carried out. Micromagnetic simulations are performed to verify our analytical results.
We present a theoretical study of heat transport in electrically insulating ferromagnetic wires containing a domain wall. In the regime of validity of continuum micromagnetism a domain wall is found to have no effect on the heat conductance. However, spin waves are found to be reflected by domain walls with widths of a few lattice spacings, which is associated with emergence of an additional spin wave bound state. The resulting domain wall heat conductance should be significant for thin films of Yttrium Iron Garnet with sharply defined magnetic domains.
The electronic properties of a particular class of domain walls in gapped graphene are investigated. We show that they can support mid-gap states which are localized in the vicinity of the domain wall and propagate along its length. With a finite density of domain walls, these states can alter the electronic properties of gapped graphene significantly. If the mid-gap band is partially filled,the domain wall can behave like a one-dimensional metal embedded in a semi-conductor, and could potentially be used as a single-channel quantum wire.
We analyze the dynamics of a domain wall in an easy-axis antiferromagnet driven by circularly polarized magnons. Magnons pass through a stationary domain wall without reflection and thus exert no force on it. However, they reverse their spin upon transmission, thereby transferring two quanta of angular momentum to the domain wall and causing it to precess. A precessing domain wall partially reflects magnons back to the source. The reflection of spin waves creates a previously identified reactive force. We point out a second mechanism of propulsion, which we term redshift: magnons passing throu…
Manipulation and trapping of magnetic skyrmions with domain walls in chiral magnetic thin films
本文研究利用Co/Pt超薄膜等手性磁性材料中的手性畴壁操控和捕获磁性斯格明子准粒子，通过定向斯格明子实现排斥存储、吸收形成不同拓扑结构，改变畴壁相位可擦除或存储斯格明子，为自旋电子学纳米器件提供新工具。
We explore the magnetic-field-driven motion of domain walls with different chiralities in thin ferromagnetic films made of Pt/Co/Pt, Au/Co/Pt, and Pt/Co/Au. From the analysis of domain wall dynamics, we extract parameters characterizing the interaction between domain walls and weak pinning disorder of the films. The variations of domain wall structure, controlled by an in-plane field, are found to modify the characteristic length-scale of pinning in strong correlation with the domain wall width, whatever its chirality and the interaction strength between domain walls and pinning defects. These…
The domain structure in in-plane magnetized Fe/Ni/W(110) films is investigated using spin-polarized low-energy electron microscopy. A novel transition of the domain wall shape from a zigzag-like pattern to straight is observed as a function of the film thickness, which is triggered by the transition of the domain wall type from out-of-plane chiral wall to in-plane Néel wall. The contribution of the Dzyaloshinskii-Moriya interaction to the wall energy is proposed to explain the transition of the domain wall shape, which is supported by Monte-Carlo simulations.
Domain Wall Networks as Skyrmion Crystals in Chiral Magnets
本文研究具有四方各向异性的手性磁体基态，发现畴壁网络是稳定基态且其畴壁结为半拓扑荷斯格明子，从而构成斯格明子晶体，并证明畴尺寸可由外磁场调控。
The effect of domain walls on electron transport has been investigated in microfabricated Fe wires (0.65 to 20 $μm$ linewidths) with controlled stripe domains. Magnetoresistance (MR) measurements as a function of domain wall density, temperature and the angle of the applied field are used to determine the low field MR contributions due to conventional sources in ferromagnetic materials and that due to the erasure of domain walls. A negative domain wall contribution to the resistivity is found. This result is discussed in light of a recent theoretical study of the effect of domain walls on quan…
Domain walls in soft permalloy strips may exhibit various equilibrium micromagnetic structures depending on the width and thickness of the strip, ranging from the well-known transverse and vortex walls in narrow and thin strips to double and triple vortex walls recently reported in wider strips [V. Estévez and L. Laurson, Phys. Rev. B {\bf 91}, 054407 (2015)]. Here we analyze the field driven dynamics of such domain walls in permalloy strips of widths from 240 nm up to 6 $μ$m, using the known equilibrium domain wall structures as initial configurations. Our micromagnetic simulations show that …
We present a field theoretical model which allows for domain walls that do not get stuck on impurities. For this purpose, we consider a generalized chiral magnet domain wall action with an impurity which couples both to a potential term as well as to the Dzyaloshinskii-Moriya interaction energy. We show that in the so-called critical coupling limit the interaction energy between two types of domain walls and the impurity vanishes. Therefore, at low velocity, such domain walls pass freely through the impurity with almost no loss of energy.
Magnetic domain walls are pinned strongly by abrupt changes in magnetic anisotropy. When driven into oscillation by a spin-polarized current, locally pinned domain walls can be exploited as tunable sources of short-wavelength spin waves. Here, we develop an analytical framework and discrete Heisenberg model to describe the static and dynamic properties of pinned domain walls with a head-to-tail magnetic structure. We focus on magnetic domain walls that are pinned by 90$^\circ$ rotations of uniaxial magnetic anisotropy. Our model captures the domain wall response to a spin-transfer torque that …
We study theoretically the current-induced magnetic domain wall motion in a metallic nanowire with perpendicular magnetic anisotropy. The anisotropy can reduce the critical current density of the domain wall motion. We explain the reduction mechanism and identify the maximal reduction conditions. This result facilitates both fundamental studies and device applications of the current- induced domain wall motion.
The charged domain walls in ferroelectric materials exhibit intriguing physical properties. We examine herein the charged-domain-wall structures in Ca$_{3-x}$Sr$_x$Ti$_2$O$_7$ using transmission electron microscopy. When viewed along the [001] axis, the wavy charged domain walls are observed over a wide range ($>$5 $μ$m). In contrast, short charged-domain-wall fragments (from 10 to 200 nm long) occur because they are intercepted and truncated by the conventional 180$^°$ domain walls. These results reveal the unusual charged domain structures in Ca$_{3-x}$Sr$_x$Ti$_2$O$_7$ and will be useful fo…
We consider Gaussian fluctuations about domain walls embedded in one- or two-dimensional spin lattices. Analytic expressions for the free energy of one domain wall are obtained. From these, the temperature dependence of experimentally relevant spatial scales -- i.e., the correlation length for spin chains and the size of magnetic domains for thin films magnetized out of plane -- are deduced. Stability of chiral order inside domain walls against thermal fluctuations is also discussed.
We present a micromagnetic study of the current-induced domain wall motion in perpendicularly magnetized Pt/Co/AlOx racetracks. We show that the domain wall velocity depends critically on the tilt angle of the wall relative to the current direction, which is determined by the combined action of the Dzyaloshinskii-Moriya interaction, damping-like, and field-like spin-orbit torques. The asymmetry of the domain wall velocity can be controlled by applying a bias-field perpendicular to the current direction as well as by the current amplitude. As the faster domain walls are expelled rapidly from th…
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